In a graphene pn junction at high magnetic field, unidirectional "snake states" are formed at the pn interface. In a clean pn junction, each snake state exists in one of the valleys of the graphene band structure, and the conductance of the junction as a whole is determined by microscopic details of the coupling between the snake states at the pn interface and quantum Hall edge states at the sample boundaries [Tworzydlo et al., Phys. Rev. B 76, 035411 (2007)]. Disorder mixes and couples the snake states. We here report a calculation of the full conductance distribution in the crossover between the clean limit and the strong disorder limit, in which the conductance distribution is given by random matrix theory [Abanin and Levitov, Science 317, 641 (2007)]. Our calculation involves an exact solution of the relevant scaling equation for the scattering matrix, and the results are formulated in terms of parameters describing the microscopic disorder potential in bulk graphene. arXiv:1607.07758v1 [cond-mat.mes-hall]

We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible non-zero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer et al., Phys. Rev. B 92, 121409 (2015).

The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use non-perturbative approach to calculate the disorder induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the imaginary frequency axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum resolved results. It is thus complementary to existing RG treatments of weak disorder in semimetals., (6) where the functions J 0 and J 1 themselves depend on m

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results confirm that the charge carrier density dependence of the Fermi velocity is negligible, validating the comparison of the fRG calculation at zero density of Bauer et al., Phys. Rev. B 92, 121409 (2015) with the experiment of Elias et al., Nat. Phys. 7, 701 (2011).

We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the Keldysh formalism, directly giving access to real-time correlation functions at finite temperature. We obtain an exact effective action for the Chern-Simons gauge fields, which is expanded to second order in the gauge field fluctations around the mean-field solution. The one-loop fermionic polarization tensor as well as the electromagnetic response tensor in random phase approximation are derived, from which we obtain the Hall conductivities for various FQH states, lying symmetrically around charge neutrality.